Motion control method based on fourth-order S curve

Abstract

The invention provides a four-order S curve-based motion control method, which comprises the following steps of: determining an optimal value of a maximum jerk slope time period, an optimal value of a maximum jerk time period, an optimal value of a maximum acceleration time period and an optimal value of a maximum speed time period; dividing into track symmetry in 15 time periods based on a 4-order S curve, and calculating a jerk slope time period value, a jerk time period value, an acceleration time period value and a speed time period value based on the 4-order S curve; determining time length values of the 15 time periods based on the jerk slope time period value, the jerk time period value, the acceleration time period value and the speed time period value; and determining the position, the speed, the acceleration, the jerk and the jerk slope of each section according to the time length values of the 15 time periods. Therefore, the acceleration is enabled to change smoothly by adopting the fourth-order S curve so as to suppress the impact on the motion platform body of the semiconductor equipment, and the position precision of the final stop position is ensured, so that the motion control performance of the whole equipment is improved.

Description

Technical Field

[0001] The present application relates to the field of motion control technology, and more specifically, to a motion control method based on a 4th-order S-curve. Background Art

[0002] The photolithography machine is an important equipment in the semiconductor manufacturing process. Its function is to accurately transfer the circuit pattern in the mask plate (also called the mask plate) to the silicon wafer or other substrate according to the predetermined size and position through the exposure process. This requires extremely high alignment accuracy between the mask plate and the silicon wafer or other substrate, which puts high demands on the motion control of various moving stages of the photolithography machine, such as the workpiece stage and the mask stage. In particular, in the scanning lithography process, it is expected that the workpiece stage and the mask stage have extremely high stability when moving synchronously.

[0003] Therefore, it is desirable to provide an improved motion control solution. Summary of the invention

[0004] An embodiment of the present application provides a motion control method based on a 4th-order S-curve, which uses a 4th-order S-curve to make the acceleration change smoothly, thereby suppressing the impact on the moving platform of the semiconductor device and ensuring the position accuracy of the final stop position, thereby improving the motion control performance of the overall device.

[0005] According to one aspect of the present application, a motion control method based on a 4th-order S-curve is provided, comprising: determining an optimal value of a maximum jerk slope time period, an optimal value of a maximum jerk time period, an optimal value of a maximum acceleration time period, and an optimal value of a maximum speed time period; based on the trajectory symmetry of the 4th-order S-curve divided into 15 time periods, based on the 4th-order S-curve, calculating a jerk slope time period value by the optimal value of the maximum jerk slope time period, calculating a jerk time period value by the optimal value of the maximum jerk slope time period and the jerk slope time period value, calculating an acceleration time period value by the optimal value of the maximum jerk slope time period, the jerk slope time period value, and the jerk time period value, and calculating a speed time period value by the optimal value of the maximum speed time period; determining time length values ​​of the 15 time periods based on the jerk slope time period value, the jerk time period value, the acceleration time period value, and the speed time period value; and determining the position, speed, acceleration, jerk, and jerk slope of each segment according to the time length values ​​of the 15 time periods.

[0006] In the above-mentioned motion control method based on the fourth-order S-curve, based on the trajectory symmetry s=s(t 15 )=2s(t 7 ), at t d Satisfy v max、a max 、j max Under the constraints:

[0007]

[0008] Otherwise, if v>v max ,but:

[0009]

[0010] if a>a max ,but:

[0011]

[0012] If j>j max ,but:

[0013] t d =j max / d max .

[0014] In the above-mentioned motion control method based on the fourth-order S-curve, based on the trajectory symmetry s=s(t 15 )=2s(t 7 ), at t j Satisfy v max 、a max Under the constraints:

[0015] 2d max t d t j 3 +10d max t d 2 t j 2 +16d max t d 3 t j +8d max t d 4 -s=0

[0016] Otherwise, if v>v max ,but:

[0017]

[0018] if a>a max ,but:

[0019] t j =a max / d max t d -td .

[0020] In the above-mentioned motion control method based on the fourth-order S-curve, based on the trajectory symmetry s=s(t 15 )=2s(t 7 ), at t a Satisfy v max Under the constraints:

[0021] (d max t d t j +d max t d 2 )t a 2 +(3d max t d t j 2 +9d max t d 2 t j +6d max t d 3 )t a +(2d max t d t j 3 +10d max t d 2 t j 2 +16d max t d 3 t j +8d max t d 4 -s)=0

[0024] Otherwise, if v>v max ,but:

[0025] t a =(v max -2d max t d 3 -3d max t d 2 t j -d max t d t j 2 ) / (d max t d t j +dmax t d 2 ).

[0026] In the above motion control method based on the fourth-order S-curve, t v =[ss(t 15 )] / v max .

[0027] In the above motion control method based on the fourth-order S-curve, T[1] = t d ; T[2] = t j ; T[3] = t d ; T[4] = t a ; T[5] = t d ; T[6] = t j ; T[7] = t d ; T[8] = t v ; T[9] = t d ; T

[10] = t j ; T

[11] = t d ; T

[12] = t a ; T

[13] = t d ; T

[14] = t j ; T

[15] = t d .

[0028] In the above-mentioned motion control method based on the fourth-order S-curve, the motion control method based on the fourth-order S-curve is used in the scanning lithography process of the lithography machine.

[0029] In the above motion control method based on the fourth-order S curve, when solving the roots of the multi-time equations in the above calculation process, the Newton iteration method is used and the initial roots are optimized, 0.1 is selected as the initial value, and the calculation accuracy is less than 0.000001.

[0030] In the above-mentioned motion control method based on the fourth-order S-curve, the time of the last trajectory point is rounded up and then added with 1 cycle time.

[0031] The motion control method based on the 4th-order S-curve provided in the embodiment of the present application can use the 4th-order S-curve to make the acceleration change smoothly, thereby suppressing the impact on the moving platform of the semiconductor device and ensuring the position accuracy of the final stop position, thereby improving the motion control performance of the overall device. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present application will become clear to those of ordinary skill in the art. The drawings in the specification are only used for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present application. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0033] Figure 1 A schematic diagram of a 3rd order S-curve is shown.

[0034] Figure 2 A schematic diagram of a 4th order S-curve is shown.

[0035] Figure 3 The diagram illustrates a schematic diagram of each time period of a 4th-order curve in a motion control method based on a 4th-order S-curve according to an embodiment of the present application.

[0036] Figure 4 The figure illustrates a schematic flow chart of a motion control method based on a 4th-order S-curve according to an embodiment of the present application. DETAILED DESCRIPTION

[0037] Below, the exemplary embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the exemplary embodiments described here.

[0038] Exemplary Methods

[0039] Since the general motion control does not require high precision, the motion control based on the trajectory planning of the third-order S curve is sufficient to meet the demand. Even in the motion control of the lithography machine, when planning the trajectory for motion control in the stepping stage, the motion control based on the trajectory planning of the third-order S curve can also meet the demand. However, in the scanning lithography process of the lithography machine, since the workpiece stage and the mask stage need to move synchronously during the alignment process, which requires extremely high stability, motion control based on trajectory planning higher than the third-order S curve should be adopted.

[0040] In addition, in the embodiment of the present application, considering that the motion control method based on the trajectory planning of the 5th-order S-curve is relatively complicated, and the trajectory planning calculation of the 5th-order S-curve is much more time-consuming than the trajectory planning calculation of the 3rd-order S-curve, a motion control scheme based on the trajectory planning of the 4th-order S-curve is selected, and further optimized on this basis so that its accuracy, equipment stability and computational efficiency all meet the requirements.

[0041] Specifically, for motion control based on trajectory planning of the third-order S curve, its motion position, motion speed and motion acceleration are continuously changing, but the motion jerk is a step change signal, so for precision semiconductor equipment such as lithography machines, it will cause certain impact wear and tear, and have a certain life impact, such as Figure 1 In contrast, motion control based on trajectory planning of the 4th-order S-curve can change the acceleration from a step signal to a continuous signal, greatly reducing the impact on the equipment and the impact on its life. That is, the impact on the moving platform of the equipment can be suppressed by smoothly changing the acceleration, as shown in Figure 2 Here, Figure 1 A schematic diagram of a 3rd order S curve is shown, and Figure 2 A schematic diagram of a 4th order S-curve is shown.

[0042] based on Figure 2 , in order to perform trajectory planning, that is, to determine the position change over time, it is necessary to calculate the time period values ​​of velocity, acceleration, jerk, and jerk slope, which can be expressed as t v , t a , t j and t d Usually, a segmented calculation method is used when performing motion control based on S-curve trajectory planning. However, in the embodiment of the present application, t is calculated by using theoretical derivation calculation instead of segmented calculation method. v , t a , t j and t d The value of is used as a constant in subsequent calculations, which can greatly simplify conventional calculations.

[0043] First, in a pre-calculation step, the optimal value d for the maximum jerk slope period is determined max , determine the optimal value j for the maximum jerk time period max , determine the optimal value a of the maximum acceleration time period max , and determine the optimal value v for the maximum speed time period max .

[0044] Then, based on the optimal value d of the maximum jerk slope time period max , the optimal value j of the maximum jerk time period max , the optimal value a of the maximum acceleration time period max , and the optimal value v of the maximum speed time period max Determine the value of each time segment of the 4th order S-curve.

[0045] Specifically, when the 4th order S curve is usually divided into 15 time periods, based on the trajectory symmetry principle, s=s(t 15 )=2s(t 7 ), where s refers to the distance (segment), which can be considered as the difference between the current position and the initial position of the S curve. 7 )=4d max t d 4 , so s=8d max t d 4 , therefore, according to Calculate t d The value of, and then according to the constraint v max 、a max 、j max Determine t d Whether the constraint conditions are met, if not, recalculate t according to the new conditions d , there are three constraints here, namely:

[0046] Maximum speed constraint: If v>v max , then recalculate

[0047] Maximum acceleration constraint: If a>a max , then recalculate

[0048] Maximum jerk constraint: If j>j max , then recalculate t d =j max / d max ;

[0049] Similarly, according to the trajectory symmetry principle s = s (t 15 )=2s(t 7 ), we can deduce:

[0050] 2d max t d t j 3 +10d max t d 2 t j 2 +16d max t d 3 t j +8d max t d 4 -s=0

[0051] From this we can calculate t j The value of , here we need to solve the positive real root, and then according to the constraint condition v max 、a max Determine t j Whether the constraint conditions are met, if not, recalculate t according to the new conditions j , there are two constraints here, namely:

[0052] Maximum speed constraint: If v>v max , then recalculate

[0053] Maximum acceleration constraint: If a>a max , then recalculate t j =a max / d max t d -t d ;

[0054] Again, according to the trajectory symmetry principle s = s (t 15 )=2s(t 7 ), we can deduce:

[0055] (d max t d t j +d max t d 2 )t a 2 +(3d max t d t j 2 +9d max t d 2 t j +6d max t d 3 )t a +(2d max t d t j 3 +10d max t d 2 t j 2 +16d max t d 3 t j +8d max t d 4 -s)=0

[0057] From this we can calculate t a The value of , and then determine whether the constraint condition v is satisfied max If it does not meet the new conditions, recalculate t a ;

[0058] Maximum speed constraint: If v>v max , then recalculate t a =(v max -2d max t d 3 -3d max t d 2 t j -d max t d t j 2 ) / (d max t d t j +d max t d 2 );

[0059] Finally, according to t v =[ss(t 15 )] / v max Calculate t v , where s is the expected distance and s(t 15 ) According to the previous t a and s are calculated, for example, as:

[0060]

[0061] Then, according to the rule of dividing the 4th order curve into 15 segments, they are set as follows: T[1] = t d ; T[2] = t j ; T[3] = t d ; T[4] = t a ; T[5] = t d ; T[6] = t j ; T[7] = t d ; T[8] = t v ; T[9] = t d ; T

[10] = t j ; T

[11] = t d ; T

[12] = t a ; T

[13] = t d ; T

[14] = t j ; T

[15] = t d .

[0062] That is, in the embodiment of the present application, t is calculated using the limit value. d , t j , t a and t v Although the principle is the same as the segmentation method, the calculation efficiency is greatly improved, and the correctness of the result can be verified through actual coding and running.

[0063] Then, according to the timing of entry at each time point, the generation method of the segment is selected, and the position, velocity, acc, jerk and d (slope of jerk) can be calculated respectively, such as Figure 3 That is, the jerk is obtained by integrating the slope of the jerk, the acceleration is obtained by integrating the jerk, the velocity is obtained by integrating the acceleration, and the position is obtained by integrating the velocity. Here, Figure 3 The diagram illustrates a schematic diagram of each time period of a 4th-order curve in a motion control method based on a 4th-order S-curve according to an embodiment of the present application.

[0064] Based on this, Figure 4 As shown, the motion control method based on the 4th order S curve according to the embodiment of the present application includes: S110, determining the optimal values ​​of the maximum jerk slope time period, the maximum jerk time period, the maximum acceleration time period and the maximum speed time period; S120, based on the trajectory symmetry of the 4th order S curve divided into 15 time periods, based on the 4th order S curve, calculating the jerk slope time period value through the optimal value of the maximum jerk slope time period, and calculating the jerk time period value through the optimal value of the maximum jerk slope time period and the jerk slope time period value, The acceleration time period value is calculated by the optimal value of the maximum jerk slope time period, the jerk slope time period value, and the jerk time period value, and the speed time period value is calculated by the optimal value of the maximum speed time period; S130, based on the jerk slope time period value, the jerk time period value, the acceleration time period value and the speed time period value, the time length values ​​of the 15 time periods are determined; and, S140, the position, speed, acceleration, jerk and jerk slope of each segment are determined according to the time length values ​​of the 15 time periods. Here, Figure 4 The figure illustrates a schematic flow chart of a motion control method based on a 4th-order S-curve according to an embodiment of the present application.

[0065] Those skilled in the art can understand that the motion control method based on the fourth-order S curve according to the embodiment of the present application can be used for the motion control of the moving stage, such as the workpiece stage and the mask stage, in the scanning lithography process of the lithography machine, and can also be used for other semiconductor devices that require precise motion control. Therefore, although the motion control of the lithography machine is used as an example for explanation in the specification of the present application, the present application is not intended to be limited to this.

[0066] As described above, the above calculation process involves solving positive real roots. In the embodiment of the present application, when solving the roots of the multi-time equation, the Newton iteration method and the method of optimizing the initial root can quickly find the positive real root, thereby improving the calculation efficiency and reliability. That is, when solving the equation, since the Newton iteration method can converge quickly, when an appropriate initial value of the iteration is selected, the calculation process can be greatly accelerated, and since the Newton iteration method adopts a numerical iteration method of successive approximation, the highest real number solution will not be missed, and it is more reliable.

[0067] For example, due to the particularity of the moving stage of the lithography machine, its travel is generally tens of millimeters, so the range (time) of the real root cannot exceed 0.1. In this way, when the parameters used for threshold judgment when solving the real root of the equation based on the Newton iteration method are selected as 0.1 as the initial value, when the calculation accuracy is less than 0.000001, only a single-digit number of iterations can quickly calculate the result (ordinary values ​​require dozens of times), which greatly speeds up the calculation process. In addition, in order to prevent excessive calculations, the number of iterations can be limited to enhance reliability.

[0068] Moreover, in the actual application of the scanning lithography process of the lithography machine, since the electrical signal is sent at a certain time interval, that is, there will be a certain discontinuity at the microscopic level, in order to achieve an accurate accuracy of <0.1 nanometers at the final displacement, the time of the last trajectory point is rounded up and then added to 1 cycle time. That is, for the t calculated above v , t a , t j and t d , because these times are not exactly at the actual delivery point, but there will be a certain deviation, although the deviation in the intermediate process can be ignored, but the final position needs to be limited, so the final theoretical time value and the actual delivery time point are required to be aligned. In this way, it will not affect the connection of each acceleration and deceleration stage too much, and it will also ensure that the error between the final displacement and the expected value is less than 0.1 nanometers.

[0069] Moreover, rounding is performed relative to the time value of each connection point. Since the number of connection points of the 4th order S curve is relatively large (15 points), there will be some precision errors. In the embodiment of the present application, rounding is performed only at the last point, and rounding is performed upward, so that there will be no situation where the position is not reached (there will be a point that exceeds an interval time, but has stopped). In other words, the motion control method based on the 4th order S curve according to the embodiment of the present application can be understood as 15 segments + 1 point, and the last point is calculated using the original condition destination position, so there is no position error, thereby ensuring the position accuracy of the final stop position and improving the motion control performance of the overall device.

[0070] Application Examples

[0071] The following shows a code example of a motion control method based on a 4th-order S-curve for motion control in a scanning lithography process of a lithography machine according to an embodiment of the present application:

[0072]

[0073]

[0074] *_t15+1 / 2.0*genScurve->j

[14] *_t15*_t15-1 / 6.0*dmax*_t15*_t15*_t15) / RATIO;

[0075] evaScurve->setacceleRATIOn=(genScurve->a

[14] +genScurve->j

[14] *_t15-1 / 2.0*dmax*_t15*_t15) / RATIO;

[0076] evaScurve->setjerk=(genScurve->j

[14] -dmax*_t15) / RATIO;

[0077] evaScurve->setd=-dmax / RATIO;

[0078] }

[0079] Through experiments, in which experimental data are conducted on position, velocity, acc, jerk, d (slope of jerk), and t (time), with experimental data of 1,000 position points, it is shown that under typical travel conditions of tens of millimeters, the final position error is less than 0.01 nanometers.

[0080] The basic principles of the present application are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present application are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present application. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, not for limitation, and the above details do not limit the present application to being implemented by adopting the above specific details.

[0081] The block diagrams of the devices, apparatuses, equipment, and systems involved in this application are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0082] It should also be noted that in the apparatus, device and method of the present application, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present application.

[0083] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present application. Therefore, the present application is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0084] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present application to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. A motion control method based on a 4th order S curve, comprising: determining an optimal value for a maximum jerk slope period, an optimal value for a maximum jerk period, an optimal value for a maximum acceleration period, and an optimal value for a maximum velocity period; Based on the trajectory symmetry of the 15 time periods divided by the 4th order S curve, based on the 4th order S curve, the jerk slope time period value is calculated by the optimal value of the maximum jerk slope time period, the jerk time period value is calculated by the optimal value of the maximum jerk slope time period and the jerk slope time period value, the acceleration time period value is calculated by the optimal value of the maximum jerk slope time period, the jerk slope time period value, and the jerk time period value, and the speed time period value is calculated by the optimal value of the maximum speed time period; determining time length values ​​of the 15 time periods based on the jerk slope time period value, the jerk time period value, the acceleration time period value, and the speed time period value; as well as The position, velocity, acceleration, jerk and jerk slope of each segment are determined according to the time length values ​​of the 15 time segments.

2. The motion control method based on the 4th order S curve according to claim 1, wherein: Based on the trajectory symmetry s=s(t 15 )=2s(t7), at t d Satisfy v max 、a max 、j max Under the constraints: Otherwise, if v>v max ,but: if a>a max ,but: If j>j max ,but: t d =j max / d max 。 3. The motion control method based on the 4th order S curve as claimed in claim 2, wherein: Based on the trajectory symmetry s=s(t 15 )=2s(t7), at t j Satisfy v max 、a max Under the constraints: 2d max t d t j 3 +10d max t d 2 t j 2 +1d max t d 3 t j +8d max t d 4 -s=0 Otherwise, if v>v max ,but: if a>a max ,but: t j =a max / d max t d -t d 。 4. The motion control method based on the 4th order S curve as claimed in claim 3, wherein: Based on the trajectory symmetry s=s(t 15 )=2s(t7), at t a Satisfy v max Under the constraints: (d max t d t j +d max t d 2 )t a 2 +(3d max t d t j 2 +9d max t d = 2 t j +6d max t d 3 )t a +(2d max t d t j 3 +10d max t d 2 t j 2 +16d max t d l 3 t j +8d max t d 4 -s)=0 Otherwise, if v>v max ,but: t a =(v max -2d max t d 3 -3d max t d 2 t j -d max t d t j 2 ) / (d max t d t j +d max t d 2 )。 5. The motion control method based on the 4th order S-curve as claimed in claim 4, wherein: t v =[s-s(t 15 )] / v max 。 6. The motion control method based on the 4th order S curve as claimed in claim 5, wherein: T[1]=t d ;T[2]=t j ;T[3]=t d ;T[4]=t a ;T[5]=t d ;T[6]=t j ;T[7]=t d ;T[8]=t v ;T[9]=t d ;T[10]=t j ;T[11]=t d ;T[12]=t a ;T[13]=t d ;T[14]=t j ;T[15]=t d 。 7. The motion control method based on the 4th order S curve according to claim 6, wherein: The motion control method based on the fourth-order S curve is used in the scanning lithography process of the lithography machine.

8. The motion control method based on the 4th order S curve according to claim 7, wherein: When finding the roots of the multi-time equations in the calculation process as described in claims 3 and 4, the Newton iteration method is used and the initial roots are optimized, 0.1 is selected as the initial value, and the calculation accuracy is less than 0.000001.

9. The motion control method based on the 4th order S curve as claimed in claim 8, wherein: The time of the last trajectory point is rounded up and then added with 1 cycle time.

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